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arXiv · 2005.03579

On Abelianity Lines in Elliptic $W$-Algebras

Jean Avan·Luc Frappat·Eric Ragoucy
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Abstract

We present a systematic derivation of the abelianity conditions for the $q$-deformed $W$-algebras constructed from the elliptic quantum algebra $\mathcal{A}_{q,p}\big(\widehat{\mathfrak{gl}}(N)_{c}\big)$. We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space ($p, q, c$). Each line is identified as an intersection of a countable number of critical surfaces obeying diophantine consistency conditions. The corresponding Poisson brackets structures are then computed for which some universal features are described.

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BibTeXRIS

Jean Avan, Luc Frappat, Eric Ragoucy. 2020-05-07. On Abelianity Lines in Elliptic $W$-Algebras. https://doi.org/10.3842/sigma.2020.094

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